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A275697 Primes p such that gcd(p-1, q-1) = q - p, where q is the next prime after p. 2
2, 3, 5, 11, 13, 17, 29, 31, 37, 41, 59, 61, 71, 73, 89, 97, 101, 107, 109, 113, 137, 149, 151, 157, 179, 181, 191, 193, 197, 227, 229, 239, 241, 269, 271, 277, 281, 311, 313, 331, 347, 349, 367, 373, 397, 401, 419, 421, 431, 433, 449, 457, 461, 521, 523 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Primes prime(k) such that prime(k) == 1 (mod A001223(k)).

Problem: are there infinitely many such primes?

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

MAPLE

N:= 1000: # to get all terms <= N

P:= select(isprime, [2, seq(i, i=3..nextprime(N), 2)]):

P[select(i -> (P[i] - 1) mod (P[i+1]-P[i]) = 0, [$1..nops(P)-1])];

MATHEMATICA

Select[Partition[Prime[Range[100]], 2, 1], GCD[#[[1]]-1, #[[2]]-1] == #[[2]]- #[[1]]&][[All, 1]] (* Harvey P. Dale, Apr 18 2018 *)

PROG

(PARI) is(n) = ispseudoprime(n) && gcd(n-1, nextprime(n+1)-1)==nextprime(n+1)-n \\ Felix Fröhlich, Aug 06 2016

CROSSREFS

Cf. A000040, A001223.

Contains A001359.

Except for 2, contained in A090190.

Sequence in context: A040044 A253110 A140549 * A127046 A127051 A127045

Adjacent sequences:  A275694 A275695 A275696 * A275698 A275699 A275700

KEYWORD

nonn

AUTHOR

Thomas Ordowski and Robert Israel, Aug 05 2016

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)